Q12.84 P - Chemistry: Molecular Nature Of Matter And Change

Question

What type of crystal lattice does each metal form? (The number of atoms per unit cell is given in parentheses.)

(a) Ni (4)

(b) Cr (2)

(c) Ca (4)

Step-by-Step Solution

Answer

The corresponding metals have the following crystal lattices:

1. Face-centered cubic unit cell
2. Body-centered cubic unit cell
3. Face-centered cubic unit cell

Step 1: The number of atoms in unit cells and their contribution.

In metal form, three types of crystal lattices are usually formed- simple (SCC), body-centered (BCC), and face-centered (FCC) cubic unit cells.

 

The atoms in the corner of the cube contribute 1/8^th to one cubic cell.

The body-centered atom contributes to the whole atom for that cell.

The face-centered atom contributes half of the unit cell.

Step 2: Subpart (a) Type of crystal lattices in Ni (4).

In FCC, 8 atoms are present in the corner of the cube and six on the corresponding faces of the cell, thus contributing a total of 4 atoms for the cell.

For Ni, the number of atoms in the unit cell is 4, thus from the above information, Ni has a face-centered unit cell.

Step 3: Subpart (b) Type of crystal lattices in Cr (2).

In BCC, 8 atoms are present in the corner of the cube and 1 in the center, thus contributing two atoms for the cell.

For Cr, the number of atoms in the unit cell is 2, thus from the above information Cr has a body-centered unit cell.

Step 4: Subpart (c) Type of crystal lattices in Ca (4).

In FCC, 8 atoms are present in the corner of the cube and six on the corresponding faces of the cell, thus contributing a total of 4 atoms for the cell.

For Ca, the number of atoms in the unit cell is 4, thus from the above information Ca has a face-centered unit cell.